With the increase of parameter α, the steady state bifurcation behaviour can be very complicated.

This result shows that the dynamics of this cellular automaton is actually complicated.

An array of complicated structures of the natural products synthesized over the last two years is also listed to serve as a convenient lead to the original literature for the prospective interested readers.

This experiment is easily carried out without time-consuming and complicated pretreatment.

Although the structure of frequency shift filter is more complicated than the time-domain filter, it uses both time correlations and frequency spectrum correlations so it can achieve better performances on separating the overlapping signals.

An infinitesimal characterization of the complexity of homogeneous spaces

A characterization of the complexity of a homogeneous space of a reductive groupG is given in terms of the mutual position of the tangent Lie algebra of the stabilizer of a generic point of and the (-1)-eigenspace of a Weyl involution of.

In particular, we prove an integral formula for the degree of an ample divisor on a variety of complexity 1, and apply this formula to computing the degree of a closed 3-dimensional orbit in any SL2-module.

Complexity of Homogeneous Spaces and Growth of Multiplicities

The complexity of a homogeneous space G/H under a reductive group G is by definition the codimension of general orbits in G/H of a Borel subgroup B\subseteq G.